Out of intergral rate laws comes half lives. The half life of a first order reaction is a usuful number; where as, the half life of a second order reaction is less usefull. But first...what is a half life?
Half life is the amount of time required for the concentration of the reactants to fall to one half its initial value.
If the reaction is a first order reaction with only one reactant the half life can be found using the following relationship.
After all, we want to know the amount of time it takes [reactant]t = 1/2 [reactant]0 (i.e. equal to half the original concentration).
ln(1/2[reactant]0) - ln[reactant]0 = -kt1/2
or
Half life for a 2nd order rxn
What is t when when [reactant]t = 1/2[reactant]0
The moral of the story is...
The half life of a 1st order reaction does not depend on the starting concentration; so, it will always be the same for the same reaction.
The half life of a 2nd order reaction depends on the starting concentration; so, it will not be the same all the time.